package org.bouncycastle.pqc.crypto.qtesla;

final class PolynomialProvablySecure
{

    /* Provably-Secure qTESLA Security Category-1 */

    public static final long[] ZETA_I_P = {                    /* 1024-Entry */

        152487987, 362708180, 151084668, 393585500, 285507339, 301982154, 215753424, 31155376,
        233716852, 465705615, 128512487, 219324660, 50229578, 153034376, 215476824, 300536066,
        335024578, 289187646, 164713195, 268061318, 189759369, 377168836, 116435874, 176113053,
        431517196, 190900734, 338220498, 464878555, 173361289, 232250039, 454096337, 436656394,
        195787662, 168565616, 114027909, 101482211, 122304260, 245339257, 270992315, 4286310,
        284182633, 281862863, 467931137, 7603533, 87296419, 467325730, 121905925, 68965750,
        7622021, 337743349, 393551614, 47124528, 159423746, 411556895, 272161997, 437233591,
        145848369, 293644567, 483816172, 151632492, 404105953, 50166550, 146739314, 412145078,
        15864543, 70750806, 129965017, 341088149, 316683907, 350635104, 130053135, 163148141,
        121505175, 321911633, 208679484, 294431751, 453314132, 108343178, 347335911, 164705047,
        162721550, 207020617, 292545544, 470584726, 172724538, 305647837, 149867383, 362637208,
        452440748, 260522302, 286994319, 24740874, 202044444, 119470626, 478104674, 80911411,
        414592412, 2221974, 246379318, 129955789, 28799678, 36003616, 152368173, 339611023,
        223510693, 291221765, 193132933, 463217793, 331552134, 325636488, 203402489, 295759306,
        248357734, 68229047, 81897305, 240159122, 118053748, 317468757, 422053445, 366729953,
        437649988, 255661703, 483132783, 73941682, 473070031, 266941830, 273715645, 293305752,
        97728261, 387416830, 466510576, 359483415, 350097663, 303812937, 61983368, 110765849,
        174098312, 288799426, 21108638, 467492225, 174686783, 248408233, 45473451, 384747267,
        405224388, 88952814, 320950556, 7845265, 96262921, 194785009, 345346400, 283984375,
        141922183, 197095618, 350922677, 11272999, 89297173, 32109806, 274225692, 315879286,
        447761615, 162801357, 472516440, 273754932, 433704551, 12277378, 129604129, 130765873,
        341928374, 97220107, 381055612, 81197393, 281134974, 179347952, 39761035, 34072176,
        156107747, 160521566, 445615052, 382999431, 114761104, 217307868, 361522659, 154828064,
        108616610, 483961979, 7594235, 235284403, 243224032, 389934638, 100293270, 300649913,
        252603238, 156952794, 476122165, 413580514, 276718826, 361292064, 361798877, 469444666,
        478187612, 366087489, 58364362, 377641792, 464279854, 238407425, 414624898, 95101086,
        321027398, 429694956, 464583265, 437187651, 60881585, 385486792, 312091683, 66834498,
        233738788, 348037644, 233604363, 107253653, 131016429, 73947604, 169670982, 290195637,
        119921194, 271135954, 190934119, 290478001, 458387655, 30555018, 243654544, 445824897,
        428159318, 284210623, 380070942, 43667456, 346591135, 469657107, 229110312, 89859525,
        279253247, 439931225, 229136222, 321034403, 246424219, 100693825, 214223676, 217294437,
        256157960, 295265349, 79251464, 286824915, 454734790, 151846826, 92265815, 248302338,
        324806913, 107169154, 198491413, 107136390, 135693521, 363861623, 129717151, 385117374,
        341459776, 364530058, 331840615, 338653108, 179941421, 145194323, 232142444, 310117875,
        245100240, 236651455, 321450096, 408132892, 459643284, 120999848, 331994388, 466033192,
        444350281, 46244984, 349366459, 47312667, 210852290, 461907423, 473508756, 243941159,
        334095768, 484392307, 87495054, 79707111, 10325325, 200821060, 83579595, 150963302,
        117650353, 241599951, 324099496, 449053341, 36312493, 53120594, 297622605, 80558972,
        378548649, 444726854, 381040843, 435710377, 437798831, 409728224, 337424109, 119488440,
        361132895, 56096923, 105509808, 62508901, 220866000, 465933834, 134955292, 165152430,
        461194453, 94958388, 126965781, 461323542, 383847206, 317476902, 163556720, 256017938,
        72928042, 371345649, 72741296, 1132229, 282268470, 212115745, 379618538, 106905134,
        239955357, 192105800, 279633365, 261297633, 471571564, 90968104, 459175544, 256276478,
        349475049, 94611089, 471946846, 339973147, 179509745, 334215655, 348294589, 246487412,
        338690430, 257410736, 386561992, 130193167, 10375815, 352823358, 66528931, 326800610,
        5109748, 350056529, 248785466, 71808467, 91140754, 240803382, 46545554, 148468313,
        217897756, 178220810, 477609665, 208790805, 132277867, 140742422, 254913327, 28667006,
        128372915, 79301382, 407186666, 89552874, 246186501, 285455129, 391678316, 275180688,
        128264018, 310322712, 204235493, 392483801, 82342680, 216812163, 464479351, 180360499,
        444647478, 203271968, 245690827, 184373912, 109600517, 224566820, 28243984, 271488557,
        21295878, 5023179, 37276402, 156173856, 216282463, 114627758, 400597776, 384792625,
        105917732, 345779139, 120948814, 379908150, 352765486, 416168777, 56042296, 349589484,
        144728793, 388255614, 261690821, 484844902, 12918385, 60552278, 302475143, 407425208,
        184843522, 76793749, 43262192, 318572606, 192724017, 307990251, 164548393, 289980843,
        119689917, 192248504, 86870040, 113677230, 207612114, 48663937, 453434248, 377339887,
        132917063, 336896801, 106411814, 268777744, 109251604, 359574042, 467613823, 362251552,
        400195434, 397227950, 447715984, 156476326, 407995653, 323955098, 143648649, 6572585,
        61447842, 60823848, 132376333, 156552612, 447237682, 3352830, 437079412, 293474358,
        288464703, 15328503, 138579659, 221291483, 380584037, 357161755, 205687364, 479414291,
        173269786, 295661628, 1098184, 377981714, 433970464, 385767379, 200391723, 463310671,
        470707303, 280545651, 289143978, 1390137, 320221838, 213802405, 52847233, 440579585,
        361337171, 467447061, 278099177, 130391690, 112618414, 24013500, 144924227, 296806074,
        251842387, 345992943, 284162718, 360902180, 420467337, 110656360, 350012131, 202820082,
        130403434, 353559391, 97646151, 331494212, 207981153, 178821640, 6093504, 174655523,
        25199097, 350851018, 171708038, 460816830, 103136904, 80524000, 275742304, 458552752,
        472541551, 190172218, 362093141, 38733526, 9645818, 67304688, 67935446, 108377230,
        311977539, 474309436, 444125532, 103441699, 3468252, 349723698, 97903160, 300076184,
        267658035, 238838767, 242177661, 26606481, 135193080, 123327558, 344360834, 367595829,
        356606282, 264791463, 257139528, 162368489, 211890949, 55564884, 438861649, 229441471,
        237272101, 233185135, 277657399, 407149255, 91300697, 479685681, 430422637, 119519807,
        421727840, 192635510, 93585631, 135381498, 18652441, 397908973, 188581729, 232327608,
        69565403, 391762415, 326530182, 441347692, 230134217, 64984929, 478944650, 351581551,
        190325639, 193670224, 149376075, 211003745, 282313407, 401282565, 142157967, 358980062,
        420121767, 23490157, 334750456, 333888004, 267502025, 165819942, 232587558, 86202250,
        302042598, 410443459, 257125477, 225677323, 414705770, 25685059, 301886182, 108044670,
        22721383, 270234733, 79875762, 146613845, 419895311, 369960062, 103044731, 31676484,
        286660070, 419993402, 364984450, 18133974, 446533052, 445715499, 406972835, 163019061,
        450202465, 241240654, 188881609, 340298195, 253414624, 384263117, 228275432, 255596801,
        10999354, 326104131, 470162945, 345212724, 481147036, 355238387, 445490028, 455415009,
        260881193, 427862585, 132654052, 18007865, 59818933, 68142229, 461931681, 213097607,
        330845761, 345671100, 445951421, 379951938, 351197187, 411141392, 7263182, 70699592,
        365421264, 376472585, 461484665, 162243510, 31855741, 293625046, 335452299, 133496651,
        449999480, 91675672, 274948339, 231546888, 5898807, 374453904, 415664585, 187816557,
        366875998, 16795888, 358324214, 67223590, 208260807, 81751761, 331910299, 126163909,
        197637544, 425142827, 380092754, 432163910, 455820426, 254980283, 256358636, 238549963,
        394492520, 207988901, 382035000, 58514991, 406817321, 338951326, 85955701, 385883363,
        199611595, 193846573, 242046917, 445871847, 194675932, 153430125, 126399473, 212399985,
        131399120, 150281168, 241101682, 424624124, 463829369, 220399539, 250758923, 286498206,
        389690457, 295269249, 379701698, 289778634, 337591505, 299401947, 408084588, 222627582,
        436090373, 268654172, 96674628, 63939283, 63956567, 362372935, 443759942, 75655989,
        451148002, 74813563, 245300859, 92113977, 235932323, 24871709, 445930061, 112311252,
        382591591, 341672267, 192081751, 227249338, 104393113, 338268986, 206994950, 319724787,
        213198392, 170478760, 37605185, 158287930, 411833228, 74675173, 290411522, 234950252,
        147659191, 477676082, 302215477, 236037294, 396241956, 90037635, 71703941, 189694446,
        127714437, 72581761, 388695298, 324058182, 307942478, 25250803, 430776557, 98441916,
        244856801, 54851167, 334050668, 381066122, 91898087, 55879503, 447270860, 473167653,
        219844498, 187193519, 266952433, 391729403, 53226126, 51780224, 371399487, 333787358,
        56263300, 280390944, 162069765, 126088217, 254997184, 219544659, 290699753, 91930445,
        262038894, 420981566, 460776098, 376255854, 282871085, 189434060, 447641051, 348987773,
        393608679, 229566111, 403901447, 471446519, 411894730, 215726740, 484920069, 409829517,
        306172231, 65880808, 272668213, 300554215, 165356547, 127919123, 432943738, 184462319,
        474779995, 312870826, 103228518, 118983222, 470656522, 71417412, 480528917, 63072121,
        276207594, 101611809, 92202812, 400978338, 316767039, 228776701, 96935521, 229917830,
        205039402, 397476586, 344074695, 398615665, 107334948, 321477097, 84224896, 289704056,
        337221600, 298175575, 221915312, 193369885, 426129039, 447853316, 54842415, 451086232,
        182463979, 451831604, 247440983, 302608727, 173057620, 189163830, 406954853, 263838955,
        390119120, 323062166, 209857219, 233847360, 397630721, 465926004, 10245195, 426687348,
        106435173, 177694955, 463447907, 18002511, 30155910, 224512318, 357311179, 265219392,
        299513685, 30291602, 60997329, 10326191, 138035293, 231111502, 414088384, 77026622,
        174972782, 4116187, 52092276, 228872080, 15308807, 286405235, 414584533, 228392331,
        399460999, 219125940, 337293712, 187192073, 183965759, 229399789, 51179285, 419512139,
        28392143, 424986565, 69672656, 202415584, 216120556, 455470549, 76078626, 278191677,
        228751917, 246802857, 389799018, 342470047, 313959017, 69383448, 340686475, 61470385,
        26192776, 409901437, 119717553, 174793260, 123425866, 250300643, 429290586, 387248439,
        183926914, 285901994, 391555377, 468207735, 22116415, 13034202, 399447558, 317569778,
        269660832, 44359608, 57347786, 225367797, 253610604, 205790505, 20120029, 285335246,
        351522795, 256987219, 358102627, 167191360, 50532216, 327731504, 369248325, 460123994,
        266415358, 194297404, 175124754, 431803266, 172719791, 347394909, 478670700, 198769524,
        172061925, 145181173, 153659180, 261113394, 234615141, 174150073, 188625016, 395363348,
        356478592, 350375496, 185431871, 422914531, 144616554, 328948119, 417580486, 132620154,
        208514724, 323125199, 169409944, 209437217, 147304756, 313577692, 467533131, 102365927,
        353952516, 47854485, 378899191, 136952166, 46435149, 470355414, 328058320, 292689847,
        24707084, 114822297, 272180086, 182640159, 7628028, 408073454, 377046674, 214221064,
        472655903, 91461227, 453378209, 459785635, 126296748, 7369666, 52466342, 269961618,
        231883972, 233439994, 228009066, 436059177, 355741338, 103186287, 391072528, 386169816,
        317017329, 449528664, 378844336, 330396197, 137599363, 20911303, 288139426, 164788880,
        266741184, 89618721, 54677577, 457226242, 208474107, 240521207, 158524358, 480614438,
        226941889, 385643536, 326188597, 389903564, 264886102, 226747931, 258540220, 407142392

    };

    public static final long[] ZETA_INVERSE_I_P = {            /* 1024-Entry */

        227437893, 259230182, 221092011, 96074549, 159789516, 100334577, 259036224, 5363675,
        327453755, 245456906, 277504006, 28751871, 431300536, 396359392, 219236929, 321189233,
        197838687, 465066810, 348378750, 155581916, 107133777, 36449449, 168960784, 99808297,
        94905585, 382791826, 130236775, 49918936, 257969047, 252538119, 254094141, 216016495,
        433511771, 478608447, 359681365, 26192478, 32599904, 394516886, 13322210, 271757049,
        108931439, 77904659, 478350085, 303337954, 213798027, 371155816, 461271029, 193288266,
        157919793, 15622699, 439542964, 349025947, 107078922, 438123628, 132025597, 383612186,
        18444982, 172400421, 338673357, 276540896, 316568169, 162852914, 277463389, 353357959,
        68397627, 157029994, 341361559, 63063582, 300546242, 135602617, 129499521, 90614765,
        297353097, 311828040, 251362972, 224864719, 332318933, 340796940, 313916188, 287208589,
        7307413, 138583204, 313258322, 54174847, 310853359, 291680709, 219562755, 25854119,
        116729788, 158246609, 435445897, 318786753, 127875486, 228990894, 134455318, 200642867,
        465858084, 280187608, 232367509, 260610316, 428630327, 441618505, 216317281, 168408335,
        86530555, 472943911, 463861698, 17770378, 94422736, 200076119, 302051199, 98729674,
        56687527, 235677470, 362552247, 311184853, 366260560, 76076676, 459785337, 424507728,
        145291638, 416594665, 172019096, 143508066, 96179095, 239175256, 257226196, 207786436,
        409899487, 30507564, 269857557, 283562529, 416305457, 60991548, 457585970, 66465974,
        434798828, 256578324, 302012354, 298786040, 148684401, 266852173, 86517114, 257585782,
        71393580, 199572878, 470669306, 257106033, 433885837, 481861926, 311005331, 408951491,
        71889729, 254866611, 347942820, 475651922, 424980784, 455686511, 186464428, 220758721,
        128666934, 261465795, 455822203, 467975602, 22530206, 308283158, 379542940, 59290765,
        475732918, 20052109, 88347392, 252130753, 276120894, 162915947, 95858993, 222139158,
        79023260, 296814283, 312920493, 183369386, 238537130, 34146509, 303514134, 34891881,
        431135698, 38124797, 59849074, 292608228, 264062801, 187802538, 148756513, 196274057,
        401753217, 164501016, 378643165, 87362448, 141903418, 88501527, 280938711, 256060283,
        389042592, 257201412, 169211074, 84999775, 393775301, 384366304, 209770519, 422905992,
        5449196, 414560701, 15321591, 366994891, 382749595, 173107287, 11198118, 301515794,
        53034375, 358058990, 320621566, 185423898, 213309900, 420097305, 179805882, 76148596,
        1058044, 270251373, 74083383, 14531594, 82076666, 256412002, 92369434, 136990340,
        38337062, 296544053, 203107028, 109722259, 25202015, 64996547, 223939219, 394047668,
        195278360, 266433454, 230980929, 359889896, 323908348, 205587169, 429714813, 152190755,
        114578626, 434197889, 432751987, 94248710, 219025680, 298784594, 266133615, 12810460,
        38707253, 430098610, 394080026, 104911991, 151927445, 431126946, 241121312, 387536197,
        55201556, 460727310, 178035635, 161919931, 97282815, 413396352, 358263676, 296283667,
        414274172, 395940478, 89736157, 249940819, 183762636, 8302031, 338318922, 251027861,
        195566591, 411302940, 74144885, 327690183, 448372928, 315499353, 272779721, 166253326,
        278983163, 147709127, 381585000, 258728775, 293896362, 144305846, 103386522, 373666861,
        40048052, 461106404, 250045790, 393864136, 240677254, 411164550, 34830111, 410322124,
        42218171, 123605178, 422021546, 422038830, 389303485, 217323941, 49887740, 263350531,
        77893525, 186576166, 148386608, 196199479, 106276415, 190708864, 96287656, 199479907,
        235219190, 265578574, 22148744, 61353989, 244876431, 335696945, 354578993, 273578128,
        359578640, 332547988, 291302181, 40106266, 243931196, 292131540, 286366518, 100094750,
        400022412, 147026787, 79160792, 427463122, 103943113, 277989212, 91485593, 247428150,
        229619477, 230997830, 30157687, 53814203, 105885359, 60835286, 288340569, 359814204,
        154067814, 404226352, 277717306, 418754523, 127653899, 469182225, 119102115, 298161556,
        70313528, 111524209, 480079306, 254431225, 211029774, 394302441, 35978633, 352481462,
        150525814, 192353067, 454122372, 323734603, 24493448, 109505528, 120556849, 415278521,
        478714931, 74836721, 134780926, 106026175, 40026692, 140307013, 155132352, 272880506,
        24046432, 417835884, 426159180, 467970248, 353324061, 58115528, 225096920, 30563104,
        40488085, 130739726, 4831077, 140765389, 15815168, 159873982, 474978759, 230381312,
        257702681, 101714996, 232563489, 145679918, 297096504, 244737459, 35775648, 322959052,
        79005278, 40262614, 39445061, 467844139, 120993663, 65984711, 199318043, 454301629,
        382933382, 116018051, 66082802, 339364268, 406102351, 215743380, 463256730, 377933443,
        184091931, 460293054, 71272343, 260300790, 228852636, 75534654, 183935515, 399775863,
        253390555, 320158171, 218476088, 152090109, 151227657, 462487956, 65856346, 126998051,
        343820146, 84695548, 203664706, 274974368, 336602038, 292307889, 295652474, 134396562,
        7033463, 420993184, 255843896, 44630421, 159447931, 94215698, 416412710, 253650505,
        297396384, 88069140, 467325672, 350596615, 392392482, 293342603, 64250273, 366458306,
        55555476, 6292432, 394677416, 78828858, 208320714, 252792978, 248706012, 256536642,
        47116464, 430413229, 274087164, 323609624, 228838585, 221186650, 129371831, 118382284,
        141617279, 362650555, 350785033, 459371632, 243800452, 247139346, 218320078, 185901929,
        388074953, 136254415, 482509861, 382536414, 41852581, 11668677, 174000574, 377600883,
        418042667, 418673425, 476332295, 447244587, 123884972, 295805895, 13436562, 27425361,
        210235809, 405454113, 382841209, 25161283, 314270075, 135127095, 460779016, 311322590,
        479884609, 307156473, 277996960, 154483901, 388331962, 132418722, 355574679, 283158031,
        135965982, 375321753, 65510776, 125075933, 201815395, 139985170, 234135726, 189172039,
        341053886, 461964613, 373359699, 355586423, 207878936, 18531052, 124640942, 45398528,
        433130880, 272175708, 165756275, 484587976, 196834135, 205432462, 15270810, 22667442,
        285586390, 100210734, 52007649, 107996399, 484879929, 190316485, 312708327, 6563822,
        280290749, 128816358, 105394076, 264686630, 347398454, 470649610, 197513410, 192503755,
        48898701, 482625283, 38740431, 329425501, 353601780, 425154265, 424530271, 479405528,
        342329464, 162023015, 77982460, 329501787, 38262129, 88750163, 85782679, 123726561,
        18364290, 126404071, 376726509, 217200369, 379566299, 149081312, 353061050, 108638226,
        32543865, 437314176, 278365999, 372300883, 399108073, 293729609, 366288196, 195997270,
        321429720, 177987862, 293254096, 167405507, 442715921, 409184364, 301134591, 78552905,
        183502970, 425425835, 473059728, 1133211, 224287292, 97722499, 341249320, 136388629,
        429935817, 69809336, 133212627, 106069963, 365029299, 140198974, 380060381, 101185488,
        85380337, 371350355, 269695650, 329804257, 448701711, 480954934, 464682235, 214489556,
        457734129, 261411293, 376377596, 301604201, 240287286, 282706145, 41330635, 305617614,
        21498762, 269165950, 403635433, 93494312, 281742620, 175655401, 357714095, 210797425,
        94299797, 200522984, 239791612, 396425239, 78791447, 406676731, 357605198, 457311107,
        231064786, 345235691, 353700246, 277187308, 8368448, 307757303, 268080357, 337509800,
        439432559, 245174731, 394837359, 414169646, 237192647, 135921584, 480868365, 159177503,
        419449182, 133154755, 475602298, 355784946, 99416121, 228567377, 147287683, 239490701,
        137683524, 151762458, 306468368, 146004966, 14031267, 391367024, 136503064, 229701635,
        26802569, 395010009, 14406549, 224680480, 206344748, 293872313, 246022756, 379072979,
        106359575, 273862368, 203709643, 484845884, 413236817, 114632464, 413050071, 229960175,
        322421393, 168501211, 102130907, 24654571, 359012332, 391019725, 24783660, 320825683,
        351022821, 20044279, 265112113, 423469212, 380468305, 429881190, 124845218, 366489673,
        148554004, 76249889, 48179282, 50267736, 104937270, 41251259, 107429464, 405419141,
        188355508, 432857519, 449665620, 36924772, 161878617, 244378162, 368327760, 335014811,
        402398518, 285157053, 475652788, 406271002, 398483059, 1585806, 151882345, 242036954,
        12469357, 24070690, 275125823, 438665446, 136611654, 439733129, 41627832, 19944921,
        153983725, 364978265, 26334829, 77845221, 164528017, 249326658, 240877873, 175860238,
        253835669, 340783790, 306036692, 147325005, 154137498, 121448055, 144518337, 100860739,
        356260962, 122116490, 350284592, 378841723, 287486700, 378808959, 161171200, 237675775,
        393712298, 334131287, 31243323, 199153198, 406726649, 190712764, 229820153, 268683676,
        271754437, 385284288, 239553894, 164943710, 256841891, 46046888, 206724866, 396118588,
        256867801, 16321006, 139386978, 442310657, 105907171, 201767490, 57818795, 40153216,
        242323569, 455423095, 27590458, 195500112, 295043994, 214842159, 366056919, 195782476,
        316307131, 412030509, 354961684, 378724460, 252373750, 137940469, 252239325, 419143615,
        173886430, 100491321, 425096528, 48790462, 21394848, 56283157, 164950715, 390877027,
        71353215, 247570688, 21698259, 108336321, 427613751, 119890624, 7790501, 16533447,
        124179236, 124686049, 209259287, 72397599, 9855948, 329025319, 233374875, 185328200,
        385684843, 96043475, 242754081, 250693710, 478383878, 2016134, 377361503, 331150049,
        124455454, 268670245, 371217009, 102978682, 40363061, 325456547, 329870366, 451905937,
        446217078, 306630161, 204843139, 404780720, 104922501, 388758006, 144049739, 355212240,
        356373984, 473700735, 52273562, 212223181, 13461673, 323176756, 38216498, 170098827,
        211752421, 453868307, 396680940, 474705114, 135055436, 288882495, 344055930, 201993738,
        140631713, 291193104, 389715192, 478132848, 165027557, 397025299, 80753725, 101230846,
        440504662, 237569880, 311291330, 18485888, 464869475, 197178687, 311879801, 375212264,
        423994745, 182165176, 135880450, 126494698, 19467537, 98561283, 388249852, 192672361,
        212262468, 219036283, 12908082, 412036431, 2845330, 230316410, 48328125, 119248160,
        63924668, 168509356, 367924365, 245818991, 404080808, 417749066, 237620379, 190218807,
        282575624, 160341625, 154425979, 22760320, 292845180, 194756348, 262467420, 146367090,
        333609940, 449974497, 457178435, 356022324, 239598795, 483756139, 71385701, 405066702,
        7873439, 366507487, 283933669, 461237239, 198983794, 225455811, 33537365, 123340905,
        336110730, 180330276, 313253575, 15393387, 193432569, 278957496, 323256563, 321273066,
        138642202, 377634935, 32663981, 191546362, 277298629, 164066480, 364472938, 322829972,
        355924978, 135343009, 169294206, 144889964, 356013096, 415227307, 470113570, 73833035,
        339238799, 435811563, 81872160, 334345621, 2161941, 192333546, 340129744, 48744522,
        213816116, 74421218, 326554367, 438853585, 92426499, 148234764, 478356092, 417012363,
        364072188, 18652383, 398681694, 478374580, 18046976, 204115250, 201795480, 481691803,
        214985798, 240638856, 363673853, 384495902, 371950204, 317412497, 290190451, 49321719,
        31881776, 253728074, 312616824, 21099558, 147757615, 295077379, 54460917, 309865060,
        369542239, 108809277, 296218744, 217916795, 321264918, 196790467, 150953535, 185442047,
        270501289, 332943737, 435748535, 266653453, 357465626, 20272498, 252261261, 454822737,
        270224689, 183995959, 200470774, 92392613, 334893445, 123269933, 333490126, 78835721

    };

    /* Provably-Secure qTESLA Security Category-3 */

    public static final long[] ZETA_III_P = {                /* 2048-Entry */

        663045521, 592864312, 129934065, 177469925, 343322489, 76003277, 514174562, 190066344,
        383213768, 787962888, 658937726, 1080673671, 1119184179, 711485619, 895353292, 741830559,
        449748398, 882352834, 210564246, 513517678, 792274530, 1106148000, 447255681, 838374925,
        817124617, 494866507, 801735296, 793510817, 270693858, 301435475, 260117255, 10836133,
        1090140236, 870237322, 519619509, 74028645, 223438873, 115296996, 731671863, 711767285,
        756344742, 432270821, 921367017, 743782190, 756600516, 403820997, 571909291, 809934428,
        12306094, 1080752961, 1103853276, 848006190, 651623616, 1066528111, 991262313, 90376233,
        1031639319, 16581402, 195692585, 764838834, 443651394, 397689573, 855192181, 464522040,
        992536780, 1065244154, 280383996, 468397118, 363648899, 30284833, 136693103, 866826704,
        684264872, 369300261, 147123393, 425272346, 947975751, 200848998, 207227922, 949139594,
        347812886, 312530409, 270384680, 1035127685, 844540200, 354908220, 399963784, 771423554,
        168982346, 111911899, 891254450, 606094727, 997954525, 531583148, 617069803, 183958096,
        133356782, 708062096, 808380329, 644973028, 1122831312, 519547216, 764125907, 320659143,
        557529771, 1016802360, 1043273438, 1045802164, 1034628659, 450715977, 741225144, 605149405,
        1012579499, 651882116, 904529967, 300080999, 629210435, 173034527, 989077200, 1078174711,
        110168090, 256388598, 610617659, 881033840, 608872901, 50037154, 640116890, 769511414,
        738741272, 92678917, 442704510, 821794500, 142894162, 370261366, 899737750, 578322223,
        983445865, 278101088, 320548969, 960437988, 847057645, 535264585, 1031091774, 384531787,
        839679409, 791760948, 937608754, 64047905, 315242491, 690211684, 304945377, 127139900,
        55322681, 615105519, 1057531084, 720717234, 1061452791, 1095429367, 975341664, 483335114,
        346985754, 486624908, 954236263, 606609353, 374493515, 1026296717, 325660087, 901013385,
        53959974, 212660347, 959289131, 1056916487, 1125908681, 840084518, 527647955, 143827226,
        1054554933, 861883427, 114992875, 332264810, 1071780030, 502142509, 205074888, 328230624,
        728399298, 6590787, 412294778, 821072942, 186833297, 86543585, 380686974, 684478338,
        685483832, 170880254, 1049509911, 299404976, 355091877, 952129776, 345588044, 357652764,
        1076734604, 924340986, 262332782, 562093746, 674846863, 869200402, 167429450, 230595565,
        379519977, 64054402, 667864494, 252591944, 174034622, 45520823, 784274107, 752467928,
        436711302, 1004905853, 329220738, 721523796, 169192713, 551217408, 907929323, 194805106,
        62131815, 68055725, 545662009, 726339771, 10612113, 878659984, 675814719, 365783377,
        951164276, 866711073, 684096262, 413270603, 702997992, 778608769, 127639044, 47216120,
        744109445, 430463358, 1117777586, 424051168, 656374939, 1103725866, 14621181, 919164722,
        915751418, 976196867, 260519617, 802701264, 977088018, 632721351, 20944803, 435584923,
        672284530, 530447301, 1080372403, 969633414, 858453527, 467086140, 377506201, 201043187,
        624606245, 356437339, 392100995, 997346375, 344147086, 1086111956, 718030456, 110621087,
        452912731, 336746546, 621211472, 795046, 794852591, 919732385, 714562897, 692647493,
        521856561, 892141810, 929164476, 178245765, 949027329, 511109867, 501815810, 855826969,
        240246307, 1090455392, 871247558, 612287417, 200668298, 658636844, 62944986, 482777398,
        714192478, 867140496, 199314763, 780516102, 571032048, 817693014, 607138429, 912533516,
        774019587, 835671643, 168024255, 449898784, 964159534, 486792883, 1119449268, 6657041,
        86939725, 764245347, 273343215, 777897095, 930426166, 788914763, 469974947, 178163195,
        519599146, 886003889, 859825363, 1024222142, 888997684, 402918616, 146815556, 742952999,
        908078470, 687435577, 647696655, 693593765, 766931890, 944985585, 394729082, 816013317,
        392951623, 65907852, 96202750, 645391372, 795224730, 402710723, 863608137, 818970673,
        545310222, 970699745, 913314065, 344644471, 195858177, 414360679, 357670948, 683445481,
        833938949, 1027656845, 191164920, 78809923, 1041045426, 73270196, 101525688, 185383095,
        583325181, 265134328, 467801210, 1096264575, 367433146, 474798672, 41386419, 8344607,
        170218721, 635545135, 668716283, 348890991, 155290659, 123249926, 769501318, 244415064,
        1050203259, 859568787, 237251392, 995643980, 522636185, 829867059, 324850649, 618298124,
        650748178, 467147593, 524674833, 341426504, 402629779, 519829789, 805279247, 494226863,
        508315225, 319600904, 48615828, 165396124, 328305874, 183239019, 878118280, 161754975,
        715041085, 746274821, 961841131, 357826469, 97008202, 885304034, 352059292, 197879468,
        25678065, 1028070136, 447949253, 962673193, 813464159, 17237594, 674670906, 959137288,
        10286769, 182827874, 439769615, 875041932, 304463252, 374894049, 749497333, 38938778,
        95615605, 323023572, 918611876, 207681758, 859164726, 97118122, 769881035, 360249017,
        507250246, 223795463, 24153203, 927058118, 178686381, 765072252, 491103160, 30816153,
        100214484, 554568910, 715304135, 93510037, 1021905527, 1045723816, 900771572, 1011589617,
        558930760, 228903927, 41675196, 857737037, 1092385029, 1067405169, 526576034, 25638952,
        1017160549, 1052660585, 364103167, 228705333, 566586884, 1126549926, 148651837, 217709216,
        614537001, 773273483, 1097591846, 480172084, 365704498, 262321659, 937989155, 1036392392,
        811974084, 132591218, 799370207, 255702709, 215218285, 632314426, 58376649, 483086198,
        401012915, 839724879, 70449719, 502867571, 757507513, 1073691794, 215293647, 725537396,
        398067214, 584143318, 392011063, 554158763, 730533625, 632408477, 259767996, 1124249847,
        432958856, 1026767843, 237644370, 29926518, 131813155, 898001983, 581765490, 215126607,
        937229093, 1030360940, 452462053, 645808548, 645402879, 379809569, 577012489, 1082786079,
        572510912, 475330285, 152788398, 690858296, 876393456, 1002942486, 67723832, 132689262,
        1030380537, 529311082, 41121650, 626066149, 866026053, 240011600, 574505003, 565608154,
        414049009, 123706126, 80739723, 326160835, 476194893, 1126100881, 646887456, 987296393,
        1119394953, 994979769, 133560363, 725327130, 850262599, 132796686, 1114247361, 1040894619,
        562914322, 641645573, 817070125, 57537779, 59054681, 878878988, 307674440, 1001013577,
        594860688, 879718195, 318482613, 698792051, 756144110, 204900318, 1031928100, 926221256,
        695955308, 662601363, 408725276, 424272249, 110402404, 535365123, 226700293, 372920839,
        1118626221, 1070521569, 639548808, 621533107, 260391977, 316354318, 362523650, 733090366,
        456807669, 113808372, 399369653, 647539514, 165899708, 312376469, 213806296, 208149196,
        937880087, 289692684, 580756218, 963782721, 1086045881, 705999228, 1115084349, 508210869,
        893248141, 1109740411, 338975294, 752813515, 622466015, 372202503, 55041759, 338412385,
        29530795, 689413481, 974303137, 605274799, 812143197, 121492617, 758223932, 200993249,
        575018581, 1039577172, 1090395670, 612284976, 414561447, 886969, 685649488, 667914411,
        183143190, 272811635, 104938162, 64626548, 404300448, 333824065, 399917080, 105374124,
        329534966, 930231830, 187994078, 772453163, 81595362, 135380677, 536704334, 787124497,
        554875178, 60344266, 790999625, 581578940, 72453408, 872892444, 204321645, 885844343,
        942736233, 12824064, 23018086, 996569940, 818486394, 1484060, 349940348, 981882207,
        855621323, 1034617940, 565456643, 745822751, 68273335, 578729865, 170455086, 173683666,
        375983003, 128070235, 982298151, 650454518, 218561113, 1063878953, 541912322, 695738038,
        232263685, 671557037, 584280432, 126161631, 394804150, 149748923, 670383088, 150214459,
        409907258, 730673023, 452696559, 556617060, 271416278, 398913344, 793695740, 603610724,
        620753264, 760650912, 867673149, 32169440, 106515963, 802984660, 859117007, 854436840,
        736728629, 789197380, 1065424969, 689713946, 980964818, 605711034, 1105012640, 552261321,
        980118632, 868407647, 247404352, 182421983, 1076188005, 324001412, 258504546, 973008126,
        458306267, 216381363, 1099063604, 172774993, 897006405, 662034826, 827348922, 213283635,
        712936407, 586286121, 133326382, 771279651, 77080161, 692598228, 272139235, 156805228,
        184634865, 216660729, 331306952, 180435518, 1098019508, 642364354, 759605128, 444205747,
        818119290, 697748488, 779633860, 1123069299, 628905992, 1093632915, 363341708, 896455329,
        653929021, 348858884, 483831705, 248783457, 50018777, 527261991, 1108955766, 683741144,
        838366046, 1040212608, 956504693, 441862460, 181267978, 415765896, 551409278, 866054366,
        855141207, 141967451, 462022373, 903388714, 5583486, 624006881, 1027131584, 127103419,
        227496735, 876597209, 1075725589, 13097576, 275925041, 46896293, 1047922947, 480370214,
        979242782, 304620097, 88645237, 157252101, 1080960020, 1019514352, 910182857, 344499049,
        841029348, 586201316, 561562804, 877577189, 774682172, 420802584, 243335866, 818233882,
        1102088786, 910997938, 394459347, 114606856, 959148981, 304978043, 15246639, 410347623,
        819777499, 304889937, 196333903, 294201539, 742724283, 136229739, 1095082129, 710673795,
        303958022, 730529672, 330937766, 290549001, 975944911, 1012630530, 940739802, 428357654,
        876150675, 270868991, 605451019, 692162505, 164423625, 414486664, 567335281, 60501334,
        301815246, 988181982, 749960008, 971794624, 1044979874, 846257184, 944403720, 1028849636,
        20676966, 402436874, 1038249855, 636703483, 52612884, 457266419, 404964279, 764097082,
        73543501, 850137726, 543909567, 478253061, 341753973, 145701153, 816141937, 150699764,
        1012159718, 996158125, 874816245, 140152812, 1046568846, 731360631, 165696325, 923351799,
        373705673, 295885033, 571437494, 323580072, 535312031, 261690954, 128330254, 678037418,
        730169337, 800223155, 493938662, 1035925088, 1086213401, 1029948847, 703929623, 1067237691,
        203498545, 260171642, 489884813, 595714326, 717921496, 379455421, 739695761, 991791615,
        1101866478, 768413486, 248059075, 641256446, 252045193, 383431807, 1098526663, 655518597,
        868514850, 975851412, 607928997, 1015436331, 219860723, 248644475, 1100013490, 1059262194,
        616750819, 706912112, 186194896, 371412253, 932777950, 605371544, 32806481, 41915372,
        942949174, 657520226, 337575994, 767026353, 795340494, 602216057, 1051603235, 38167611,
        383256063, 961974657, 643676937, 850900578, 1033468109, 791020067, 602254362, 742154500,
        5280825, 557072845, 260014823, 274231000, 957875719, 620840911, 468091423, 844999033,
        1097180885, 635575570, 741694428, 564249983, 1015743243, 179096376, 326642449, 737067396,
        404230544, 164870855, 233971733, 25568965, 480191729, 304346683, 43284571, 600295394,
        805273167, 1081440213, 132076275, 660273218, 115344223, 436181422, 581442439, 521590088,
        278258022, 1016124223, 326820478, 833856285, 578613123, 981790341, 912622887, 677878660,
        983305736, 582146018, 50261960, 421861087, 688852042, 1053015424, 638857404, 13988561,
        613374169, 246804474, 354822706, 755945338, 48594230, 1112837032, 490266853, 331336539,
        573470525, 482415512, 1066189384, 480749813, 340470541, 1087888528, 866254054, 328905420,
        282987588, 772186429, 280721545, 827109021, 1065603359, 319039186, 632282960, 368180744,
        103743324, 1039700039, 944775691, 35416271, 876336840, 387995308, 744351857, 1024873450,
        846245765, 488549456, 793960147, 360822038, 1047746824, 70006457, 1081240530, 845224049,
        158270603, 1040065115, 109153922, 842769347, 357450022, 745529551, 127101430, 1013053569,
        653900906, 1066692138, 1026185333, 40127076, 888550251, 1074046165, 859190733, 172044729,
        232991700, 856026028, 181368869, 11312168, 965826001, 718641942, 140897415, 300107020,
        760832029, 454871649, 538869148, 209839945, 603404196, 1070516093, 362685617, 594598150,
        706680144, 248566695, 624350428, 687354425, 108825926, 996763990, 768570600, 192652503,
        1030980703, 285993613, 678456384, 666912839, 636939881, 724986064, 567331335, 1109690969,
        786490830, 1041275289, 13569330, 310803565, 1018122073, 236560398, 625689685, 227532759,
        773302523, 275485190, 151580837, 1097590370, 43338286, 709601963, 530263051, 696952520,
        591327015, 779208675, 900380693, 779322099, 365008051, 816626432, 9177437, 715814813,
        951132001, 978726879, 539618044, 330049876, 794850808, 75659606, 535871088, 1117571277,
        1035668574, 737539534, 638053030, 1067376479, 817653745, 608323193, 952285144, 489088626,
        643974231, 1100308604, 80188084, 1009055308, 528621558, 845717932, 574893980, 185963698,
        304405106, 254075674, 885653667, 125272317, 310803515, 431578311, 49069840, 734649900,
        64565269, 68004786, 877673289, 927546004, 379372125, 179774076, 313581255, 48547291,
        669540902, 805507558, 458763285, 808407028, 467495228, 200042934, 286655832, 204624339,
        1076184783, 580415818, 422842319, 130214533, 1019327141, 196299734, 544501682, 1039357725,
        139924087, 1079672537, 517801387, 1103773407, 832398676, 971715180, 249998343, 17982966,
        226812113, 1056456541, 429118671, 1115368643, 731996995, 114969826, 90081103, 503306049,
        601600644, 221645888, 419902454, 366845662, 668188540, 595203705, 289744999, 311876332,
        708499030, 814702169, 1038171811, 305413430, 1025269191, 401153805, 524933941, 244137773,
        690611117, 1006016675, 368084114, 695256047, 400388115, 315582560, 240063473, 316625045,
        193016450, 444532677, 490320790, 1007751505, 809310640, 335632874, 932973140, 879894932,
        664689650, 582802605, 524248338, 381467584, 15568620, 102853205, 344510143, 244997234,
        228087680, 804700227, 33671368, 202173391, 810352194, 941527027, 107007723, 250295846,
        439491161, 385750316, 881611329, 305721499, 489662560, 253590441, 574217985, 187749275,
        767834897, 577560416, 666585061, 536277466, 31104595, 459368906, 738728273, 395846485,
        915511988, 152055976, 123475832, 434555954, 708682317, 873350950, 733405860, 594180445,
        508539260, 411702537, 525230789, 245498406, 807139759, 421829267, 576175978, 671688378,
        586113326, 717964200, 549178465, 340455344, 177498005, 185915353, 758077402, 35174925,
        62477885, 432126554, 865525725, 94991243, 953163796, 64489669, 63466463, 1027121609,
        603180773, 102927367, 328204523, 849484682, 1106252192, 166218129, 336284946, 115841434,
        394987097, 1071354740, 1124188058, 756569276, 1109657140, 693362574, 582653179, 356054504,
        10684879, 43556307, 683161419, 43248060, 311516690, 801263962, 259313122, 1076460000,
        627348913, 723691023, 1029014449, 1100617454, 910402911, 804049172, 439314326, 277694586,
        89508968, 45373766, 191679221, 573131182, 602365665, 620254956, 594424107, 763083130,
        984103431, 746523686, 419387264, 1030279302, 774892955, 242854266, 102748733, 633218020,
        205014651, 835462852, 458575555, 34062189, 765679808, 999547926, 509921953, 785947219,
        966902522, 639941920, 244960006, 581685840, 1052422889, 674992133, 61665140, 451012255,
        122965849, 190085617, 748838858, 349331162, 529980624, 16193587, 34516478, 42504381,
        160246364, 173535194, 187379517, 111011381, 365394663, 102220644, 699473271, 366177836,
        81692890, 659930501, 36322222, 896361190, 473670263, 1039987458, 412734344, 864218684,
        138309539, 146538307, 1101721292, 898028054, 727055521, 601140835, 577133426, 451632863,
        725601236, 388561051, 696130927, 299179408, 194132814, 104549843, 919472671, 900644523,
        848766532, 557407329, 506005527, 529295823, 637231568, 840578154, 40752048, 1043021730,
        940132528, 1635875, 390473136, 36409813, 938731454, 1005273567, 169556667, 456362115,
        968015234, 385125443, 1033592386, 622268544, 824710397, 811874465, 1126356395, 1030647864,
        1027801728, 1032615842, 990780079, 340414618, 431920306, 797512392, 36624143, 1039964580,
        78368304, 725419125, 1031876274, 545277986, 400681087, 824700406, 916868477, 979226643,
        327065594, 666022464, 692190875, 241031536, 486380927, 271722557, 903843361, 141586809,
        747887461, 634534510, 613428929, 35052951, 519999706, 907994356, 122720932, 47771789,
        111045658, 101409844, 478385667, 160271513, 709331396, 407803014, 233222181, 446853856,
        325464420, 902760210, 272094082, 341360162, 749117421, 560701701, 963877946, 787641615,
        205947725, 590645393, 232274153, 623635766, 912309623, 1120569701, 620395638, 104547179,
        326785462, 462547537, 940416330, 25839620, 19867751, 37744827, 852776583, 515439522,
        254321646, 368159144, 977334258, 457474804, 545693728, 590432747, 485742318, 929078943,
        737942351, 275516935, 808617222, 720700675, 172457394, 549776288, 773237950, 425343903,
        106571968, 735846275, 60428193, 122914286, 749764808, 987165321, 38777778, 78068884,
        255797430, 533180457, 948660956, 48180746, 1126178511, 529625145, 556629751, 638195644,
        832146389, 336969603, 525037491, 33022927, 179961503, 1111138669, 8606225, 744603862,
        831709431, 936738778, 976276214, 628380488, 186998645, 1058798754, 681993880, 653924606,
        946881757, 648359538, 739466740, 91286181, 294298084, 874448181, 197552840, 1095208028,
        1044083721, 391228026, 525623627, 1098872860, 195023028, 787479821, 623295468, 953049875,
        598245883, 53206653, 107774100, 1118437046, 444804586, 736921099, 245341091, 386750976,
        133313309, 679691423, 1106023536, 311728621, 298633293, 401684808, 243635798, 110079800,
        995741344, 323549381, 934619946, 561564543, 318482785, 437414717, 954436048, 120567824,
        939556676, 96791826, 457592630, 938550164, 338458435, 235369986, 520146590, 367137669,
        215447981, 816673608, 388257556, 367337840, 505745620, 16797457, 625598745, 670629880,
        254936589, 910270385, 42251434, 163010455, 35446687, 313308255, 882198755, 1020005685,
        629715947, 45305629, 160442570, 751826615, 839359276, 665790727, 1126866480, 206409968,
        243347643, 601811321, 987009162, 748255207, 204576339, 60528047, 215906665, 956509919,
        298034351, 23754044, 490568798, 458549410, 38365707, 66017494, 289322020, 23546127,
        1110422453, 430589196, 451259509, 452129088, 246026906, 479959331, 657705765, 154141097,
        545145366, 756619911, 1056054068, 305614614, 982437349, 733683110, 356219317, 138617825,
        1077109241, 367006768, 107952142, 792745355, 1101149620, 190430549, 642564451, 1027811321,
        529836063, 856677079, 136144741, 193585315, 759745460, 929992250, 670307004, 1127656802,
        1006741766, 845736365, 936834519, 1017230852, 281391123, 580173947, 30327752, 1121201269,
        1055919747, 182909919, 160816233, 602222114, 380162230, 868238592, 238843489, 626593576,
        827265325, 474165116, 237320246, 663594943, 436318864, 1049025048, 70720879, 971089740,
        88817691, 635640003, 121885571, 243941023, 2431313, 941718254, 799204753, 612476838,
        941429841, 218425031, 62583588, 843195067, 826107237, 360474616, 699278259, 879607149,
        103065937, 68048433, 88684453, 368247280, 352557675, 958077844, 188716852, 142753212,
        187289952, 1075600752, 538047877, 79021856, 72991411, 855788038, 872392901, 230685283,
        684292160, 1006193052, 389933214, 858196548, 879451470, 275454910, 233947442, 798039506,
        522351014, 1028810225, 973496946, 459028464, 716757179, 299354781, 303032004, 378782749,
        726394798, 822245773, 1112315820, 572181708, 792445736, 354854796, 391571531, 1120313604,
        948219264, 683224878, 109721560, 210780537, 877361416, 837335205, 829228039, 710692263,
        336548681, 1113948080, 500533488, 561629043, 1004877220, 538880595, 121199664, 933983782,
        1012189335, 466644222, 948695748, 1030237630, 409196123, 831874921, 209931563, 472212875,
        667493959, 374083498, 121993645, 135468879, 743372774, 445381601, 1056162737, 535313411,
        731504361, 106330271, 449811720, 1025526021, 538706550, 384586636, 672759140, 214035474,
        1061388936, 1083928033, 581161697, 343521559, 467089784, 918062822, 197840310, 276992034,
        267922106, 626045501, 689381922, 1031751565, 453082931, 703374420, 543907459, 1101013667,
        158907990, 531648771, 96624556, 1107736421, 653786417, 1020275778, 1100295652, 1080331394,
        934499233, 1103133235, 665774139, 760309263, 583529543, 927074230, 109488746, 759686422,
        658349346, 1121943871, 528665116, 800822916, 210288486, 526666123, 265162098, 797138998,
        225170105, 773601444, 1074231036, 358050025, 792486275, 559918288, 931510368, 283561253,
        929909084, 643871325, 165045098, 236482168, 27010690, 947252425, 762156229, 403915775,
        226420583, 111771291, 457403715, 390913388, 417791477, 1051596236, 218412938, 231310973,
        913814997, 1010678562, 1061436357, 402561769, 46161499, 194906871, 1106996555, 1044025883,
        84769121, 958130074, 458164325, 75716319, 742943036, 662710618, 1015724782, 541305935,
        887985887, 374173602, 667853276, 1118405527, 888897413, 806335907, 483810195, 94681964,
        932049061, 419630532, 863884216, 258267823, 871542447, 748276380, 1089602035, 956286084,
        452661681, 297101315, 292838603, 602202013, 59322052, 868600049, 695946675, 1119453722,
        369279180, 571163895, 1076824823, 613633165, 1105924843, 970753160, 38059756, 230436803,
        993075206, 825136859, 772252886, 665426090, 252341082, 81169114, 15411109, 1109435384,
        169742336, 879343295, 637603710, 1050610062, 543393828, 360888011, 622980636, 538625088,
        384365656, 954674344, 672395534, 822045489, 271453575, 379517678, 745140555, 64423305,
        132805764, 730783710, 818513567, 1062263522, 633828399, 609441394, 952235218, 443525262,
        408766329, 154648340, 321016488, 39971097, 975003097, 115001826, 929799112, 1079586908,
        630403891, 883673758, 1017692831, 982184607, 1052333730, 732655912, 673402471, 144580658,
        776541469, 599807837, 897876410, 750409126, 408883399, 800706291, 525848844, 1043397101,
        546417436, 927622216, 923472422, 126273770, 976796416, 301390002, 640312848, 64953087,
        850801014, 80099312, 344764299, 166353727, 304339056, 563820482, 620610256, 95176064,
        436429135, 450761768, 1080607344, 554114394, 1051016002, 1094965858, 1044316801, 90082309,
        802170370, 785939405, 96092255, 481999812, 399399466, 798786453, 1069910963, 1075397160,
        645632403, 721614722, 81169724, 16732546, 256145620, 1032181185, 858152279, 261506136,
        939613769, 1109259166, 1072545109, 893701664, 1076290454, 94376212, 1129486743, 496007349,
        461211004, 215869774, 903345586, 185658758, 769007243, 973105742, 843449005, 531620573,
        115498344, 118893063, 1080559132, 289993254, 729094212, 100228973, 970141524, 88018590,
        401752692, 490667846, 120206196, 1053373040, 927137503, 109156130, 1099960359, 852051778,
        542020710, 890761046, 935484975, 503476669, 247175418, 137646228, 122463313, 1098625172,
        313612773, 1045687932, 942418016, 223296002, 613265129, 618070459, 210263615, 258537008,
        687201993, 1069972265, 1092070505, 209044958, 705866604, 959480062, 37107231, 530334549,
        940857114, 888162459, 550603427, 833686010, 914377969, 777858517, 823074720, 257780639,
        682005406, 79684712, 1108405948, 546085914, 695245394, 296369184, 90008780, 876596576,
        1060844810, 971909901, 180162302, 155422312, 913147941, 572392352, 172449506, 707256652,
        379461286, 396142844, 341990080, 626969834, 156354367, 614031487, 682424885, 1092771510,
        881893810, 1087158911, 85380176, 1044830162, 986021749, 619772632, 829678380, 1095084953,
        726141659, 941134286, 949047185, 1013348374, 17076281, 979953556, 730262704, 692286875,
        723405610, 879517616, 639675138, 319980056, 711102461, 564387868, 1089317723, 659400607,
        372246588, 1035423048, 766956675, 186444638, 504211183, 871579167, 64189114, 905789437

    };

    public static final long[] ZETA_INVERSE_III_P = {        /* 2048-Entry */

        1065536839, 258146786, 625514770, 943281315, 362769278, 94302905, 757479365, 470325346,
        40408230, 565338085, 418623492, 809745897, 490050815, 250208337, 406320343, 437439078,
        399463249, 149772397, 1112649672, 116377579, 180678768, 188591667, 403584294, 34641000,
        300047573, 509953321, 143704204, 84895791, 1044345777, 42567042, 247832143, 36954443,
        447301068, 515694466, 973371586, 502756119, 787735873, 733583109, 750264667, 422469301,
        957276447, 557333601, 216578012, 974303641, 949563651, 157816052, 68881143, 253129377,
        1039717173, 833356769, 434480559, 583640039, 21320005, 1050041241, 447720547, 871945314,
        306651233, 351867436, 215347984, 296039943, 579122526, 241563494, 188868839, 599391404,
        1092618722, 170245891, 423859349, 920680995, 37655448, 59753688, 442523960, 871188945,
        919462338, 511655494, 516460824, 906429951, 187307937, 84038021, 816113180, 31100781,
        1007262640, 992079725, 882550535, 626249284, 194240978, 238964907, 587705243, 277674175,
        29765594, 1020569823, 202588450, 76352913, 1009519757, 639058107, 727973261, 1041707363,
        159584429, 1029496980, 400631741, 839732699, 49166821, 1010832890, 1014227609, 598105380,
        286276948, 156620211, 360718710, 944067195, 226380367, 913856179, 668514949, 633718604,
        239210, 1035349741, 53435499, 236024289, 57180844, 20466787, 190112184, 868219817,
        271573674, 97544768, 873580333, 1112993407, 1048556229, 408111231, 484093550, 54328793,
        59814990, 330939500, 730326487, 647726141, 1033633698, 343786548, 327555583, 1039643644,
        85409152, 34760095, 78709951, 575611559, 49118609, 678964185, 693296818, 1034549889,
        509115697, 565905471, 825386897, 963372226, 784961654, 1049626641, 278924939, 1064772866,
        489413105, 828335951, 152929537, 1003452183, 206253531, 202103737, 583308517, 86328852,
        603877109, 329019662, 720842554, 379316827, 231849543, 529918116, 353184484, 985145295,
        456323482, 397070041, 77392223, 147541346, 112033122, 246052195, 499322062, 50139045,
        199926841, 1014724127, 154722856, 1089754856, 808709465, 975077613, 720959624, 686200691,
        177490735, 520284559, 495897554, 67462431, 311212386, 398942243, 996920189, 1065302648,
        384585398, 750208275, 858272378, 307680464, 457330419, 175051609, 745360297, 591100865,
        506745317, 768837942, 586332125, 79115891, 492122243, 250382658, 959983617, 20290569,
        1114314844, 1048556839, 877384871, 464299863, 357473067, 304589094, 136650747, 899289150,
        1091666197, 158972793, 23801110, 516092788, 52901130, 558562058, 760446773, 10272231,
        433779278, 261125904, 1070403901, 527523940, 836887350, 832624638, 677064272, 173439869,
        40123918, 381449573, 258183506, 871458130, 265841737, 710095421, 197676892, 1035043989,
        645915758, 323390046, 240828540, 11320426, 461872677, 755552351, 241740066, 588420018,
        114001171, 467015335, 386782917, 1054009634, 671561628, 171595879, 1044956832, 85700070,
        22729398, 934819082, 1083564454, 727164184, 68289596, 119047391, 215910956, 898414980,
        911313015, 78129717, 711934476, 738812565, 672322238, 1017954662, 903305370, 725810178,
        367569724, 182473528, 1102715263, 893243785, 964680855, 485854628, 199816869, 846164700,
        198215585, 569807665, 337239678, 771675928, 55494917, 356124509, 904555848, 332586955,
        864563855, 603059830, 919437467, 328903037, 601060837, 7782082, 471376607, 370039531,
        1020237207, 202651723, 546196410, 369416690, 463951814, 26592718, 195226720, 49394559,
        29430301, 109450175, 475939536, 21989532, 1033101397, 598077182, 970817963, 28712286,
        585818494, 426351533, 676643022, 97974388, 440344031, 503680452, 861803847, 852733919,
        931885643, 211663131, 662636169, 786204394, 548564256, 45797920, 68337017, 915690479,
        456966813, 745139317, 591019403, 104199932, 679914233, 1023395682, 398221592, 594412542,
        73563216, 684344352, 386353179, 994257074, 1007732308, 755642455, 462231994, 657513078,
        919794390, 297851032, 720529830, 99488323, 181030205, 663081731, 117536618, 195742171,
        1008526289, 590845358, 124848733, 568096910, 629192465, 15777873, 793177272, 419033690,
        300497914, 292390748, 252364537, 918945416, 1020004393, 446501075, 181506689, 9412349,
        738154422, 774871157, 337280217, 557544245, 17410133, 307480180, 403331155, 750943204,
        826693949, 830371172, 412968774, 670697489, 156229007, 100915728, 607374939, 331686447,
        895778511, 854271043, 250274483, 271529405, 739792739, 123532901, 445433793, 899040670,
        257333052, 273937915, 1056734542, 1050704097, 591678076, 54125201, 942436001, 986972741,
        941009101, 171648109, 777168278, 761478673, 1041041500, 1061677520, 1026660016, 250118804,
        430447694, 769251337, 303618716, 286530886, 1067142365, 911300922, 188296112, 517249115,
        330521200, 188007699, 1127294640, 885784930, 1007840382, 494085950, 1040908262, 158636213,
        1059005074, 80700905, 693407089, 466131010, 892405707, 655560837, 302460628, 503132377,
        890882464, 261487361, 749563723, 527503839, 968909720, 946816034, 73806206, 8524684,
        1099398201, 549552006, 848334830, 112495101, 192891434, 283989588, 122984187, 2069151,
        459418949, 199733703, 369980493, 936140638, 993581212, 273048874, 599889890, 101914632,
        487161502, 939295404, 28576333, 336980598, 1021773811, 762719185, 52616712, 991108128,
        773506636, 396042843, 147288604, 824111339, 73671885, 373106042, 584580587, 975584856,
        472020188, 649766622, 883699047, 677596865, 678466444, 699136757, 19303500, 1106179826,
        840403933, 1063708459, 1091360246, 671176543, 639157155, 1105971909, 831691602, 173216034,
        913819288, 1069197906, 925149614, 381470746, 142716791, 527914632, 886378310, 923315985,
        2859473, 463935226, 290366677, 377899338, 969283383, 1084420324, 500010006, 109720268,
        247527198, 816417698, 1094279266, 966715498, 1087474519, 219455568, 874789364, 459096073,
        504127208, 1112928496, 623980333, 762388113, 741468397, 313052345, 914277972, 762588284,
        609579363, 894355967, 791267518, 191175789, 672133323, 1032934127, 190169277, 1009158129,
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}
